// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>
// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>
// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef KRONECKER_TENSOR_PRODUCT_H
#define KRONECKER_TENSOR_PRODUCT_H

namespace Eigen {

/*!
 * \ingroup KroneckerProduct_Module
 *
 * \brief The base class of dense and sparse Kronecker product.
 *
 * \tparam Derived is the derived type.
 */
template <typename Derived> class KroneckerProductBase : public ReturnByValue<Derived>
{
private:
    typedef typename internal::traits<Derived> Traits;
    typedef typename Traits::Scalar Scalar;

protected:
    typedef typename Traits::Lhs Lhs;
    typedef typename Traits::Rhs Rhs;

public:
    /*! \brief Constructor. */
    KroneckerProductBase(const Lhs& A, const Rhs& B) : m_A(A), m_B(B) {}

    inline Index rows() const { return m_A.rows() * m_B.rows(); }
    inline Index cols() const { return m_A.cols() * m_B.cols(); }

    /*!
     * This overrides ReturnByValue::coeff because this function is
     * efficient enough.
     */
    Scalar coeff(Index row, Index col) const { return m_A.coeff(row / m_B.rows(), col / m_B.cols()) * m_B.coeff(row % m_B.rows(), col % m_B.cols()); }

    /*!
     * This overrides ReturnByValue::coeff because this function is
     * efficient enough.
     */
    Scalar coeff(Index i) const
    {
        EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
        return m_A.coeff(i / m_A.size()) * m_B.coeff(i % m_A.size());
    }

protected:
    typename Lhs::Nested m_A;
    typename Rhs::Nested m_B;
};

/*!
 * \ingroup KroneckerProduct_Module
 *
 * \brief Kronecker tensor product helper class for dense matrices
 *
 * This class is the return value of kroneckerProduct(MatrixBase,
 * MatrixBase). Use the function rather than construct this class
 * directly to avoid specifying template prarameters.
 *
 * \tparam Lhs  Type of the left-hand side, a matrix expression.
 * \tparam Rhs  Type of the rignt-hand side, a matrix expression.
 */
template <typename Lhs, typename Rhs> class KroneckerProduct : public KroneckerProductBase<KroneckerProduct<Lhs, Rhs>>
{
private:
    typedef KroneckerProductBase<KroneckerProduct> Base;
    using Base::m_A;
    using Base::m_B;

public:
    /*! \brief Constructor. */
    KroneckerProduct(const Lhs& A, const Rhs& B) : Base(A, B) {}

    /*! \brief Evaluate the Kronecker tensor product. */
    template <typename Dest> void evalTo(Dest& dst) const;
};

/*!
 * \ingroup KroneckerProduct_Module
 *
 * \brief Kronecker tensor product helper class for sparse matrices
 *
 * If at least one of the operands is a sparse matrix expression,
 * then this class is returned and evaluates into a sparse matrix.
 *
 * This class is the return value of kroneckerProduct(EigenBase,
 * EigenBase). Use the function rather than construct this class
 * directly to avoid specifying template prarameters.
 *
 * \tparam Lhs  Type of the left-hand side, a matrix expression.
 * \tparam Rhs  Type of the rignt-hand side, a matrix expression.
 */
template <typename Lhs, typename Rhs> class KroneckerProductSparse : public KroneckerProductBase<KroneckerProductSparse<Lhs, Rhs>>
{
private:
    typedef KroneckerProductBase<KroneckerProductSparse> Base;
    using Base::m_A;
    using Base::m_B;

public:
    /*! \brief Constructor. */
    KroneckerProductSparse(const Lhs& A, const Rhs& B) : Base(A, B) {}

    /*! \brief Evaluate the Kronecker tensor product. */
    template <typename Dest> void evalTo(Dest& dst) const;
};

template <typename Lhs, typename Rhs> template <typename Dest> void KroneckerProduct<Lhs, Rhs>::evalTo(Dest& dst) const
{
    const int BlockRows = Rhs::RowsAtCompileTime, BlockCols = Rhs::ColsAtCompileTime;
    const Index Br = m_B.rows(), Bc = m_B.cols();
    for (Index i = 0; i < m_A.rows(); ++i)
        for (Index j = 0; j < m_A.cols(); ++j) Block<Dest, BlockRows, BlockCols>(dst, i * Br, j * Bc, Br, Bc) = m_A.coeff(i, j) * m_B;
}

template <typename Lhs, typename Rhs> template <typename Dest> void KroneckerProductSparse<Lhs, Rhs>::evalTo(Dest& dst) const
{
    Index Br = m_B.rows(), Bc = m_B.cols();
    dst.resize(this->rows(), this->cols());
    dst.resizeNonZeros(0);

    // 1 - evaluate the operands if needed:
    typedef typename internal::nested_eval<Lhs, Dynamic>::type Lhs1;
    typedef typename internal::remove_all<Lhs1>::type Lhs1Cleaned;
    const Lhs1 lhs1(m_A);
    typedef typename internal::nested_eval<Rhs, Dynamic>::type Rhs1;
    typedef typename internal::remove_all<Rhs1>::type Rhs1Cleaned;
    const Rhs1 rhs1(m_B);

    // 2 - construct respective iterators
    typedef Eigen::InnerIterator<Lhs1Cleaned> LhsInnerIterator;
    typedef Eigen::InnerIterator<Rhs1Cleaned> RhsInnerIterator;

    // compute number of non-zeros per innervectors of dst
    {
        // TODO VectorXi is not necessarily big enough!
        VectorXi nnzA = VectorXi::Zero(Dest::IsRowMajor ? m_A.rows() : m_A.cols());
        for (Index kA = 0; kA < m_A.outerSize(); ++kA)
            for (LhsInnerIterator itA(lhs1, kA); itA; ++itA) nnzA(Dest::IsRowMajor ? itA.row() : itA.col())++;

        VectorXi nnzB = VectorXi::Zero(Dest::IsRowMajor ? m_B.rows() : m_B.cols());
        for (Index kB = 0; kB < m_B.outerSize(); ++kB)
            for (RhsInnerIterator itB(rhs1, kB); itB; ++itB) nnzB(Dest::IsRowMajor ? itB.row() : itB.col())++;

        Matrix<int, Dynamic, Dynamic, ColMajor> nnzAB = nnzB * nnzA.transpose();
        dst.reserve(VectorXi::Map(nnzAB.data(), nnzAB.size()));
    }

    for (Index kA = 0; kA < m_A.outerSize(); ++kA)
    {
        for (Index kB = 0; kB < m_B.outerSize(); ++kB)
        {
            for (LhsInnerIterator itA(lhs1, kA); itA; ++itA)
            {
                for (RhsInnerIterator itB(rhs1, kB); itB; ++itB)
                {
                    Index i = itA.row() * Br + itB.row(), j = itA.col() * Bc + itB.col();
                    dst.insert(i, j) = itA.value() * itB.value();
                }
            }
        }
    }
}

namespace internal {

    template <typename _Lhs, typename _Rhs> struct traits<KroneckerProduct<_Lhs, _Rhs>>
    {
        typedef typename remove_all<_Lhs>::type Lhs;
        typedef typename remove_all<_Rhs>::type Rhs;
        typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
        typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;

        enum
        {
            Rows = size_at_compile_time<traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime>::ret,
            Cols = size_at_compile_time<traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime>::ret,
            MaxRows = size_at_compile_time<traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime>::ret,
            MaxCols = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret
        };

        typedef Matrix<Scalar, Rows, Cols> ReturnType;
    };

    template <typename _Lhs, typename _Rhs> struct traits<KroneckerProductSparse<_Lhs, _Rhs>>
    {
        typedef MatrixXpr XprKind;
        typedef typename remove_all<_Lhs>::type Lhs;
        typedef typename remove_all<_Rhs>::type Rhs;
        typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
        typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind,
                                                    typename traits<Rhs>::StorageKind,
                                                    scalar_product_op<typename Lhs::Scalar, typename Rhs::Scalar>>::ret StorageKind;
        typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;

        enum
        {
            LhsFlags = Lhs::Flags,
            RhsFlags = Rhs::Flags,

            RowsAtCompileTime = size_at_compile_time<traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime>::ret,
            ColsAtCompileTime = size_at_compile_time<traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime>::ret,
            MaxRowsAtCompileTime = size_at_compile_time<traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime>::ret,
            MaxColsAtCompileTime = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret,

            EvalToRowMajor = (int(LhsFlags) & int(RhsFlags) & RowMajorBit),
            RemovedBits = ~(EvalToRowMajor ? 0 : RowMajorBit),

            Flags = ((int(LhsFlags) | int(RhsFlags)) & HereditaryBits & RemovedBits) | EvalBeforeNestingBit,
            CoeffReadCost = HugeCost
        };

        typedef SparseMatrix<Scalar, 0, StorageIndex> ReturnType;
    };

}  // end namespace internal

/*!
 * \ingroup KroneckerProduct_Module
 *
 * Computes Kronecker tensor product of two dense matrices
 *
 * \warning If you want to replace a matrix by its Kronecker product
 *          with some matrix, do \b NOT do this:
 * \code
 * A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
 * \endcode
 * instead, use eval() to work around this:
 * \code
 * A = kroneckerProduct(A,B).eval();
 * \endcode
 *
 * \param a  Dense matrix a
 * \param b  Dense matrix b
 * \return   Kronecker tensor product of a and b
 */
template <typename A, typename B> KroneckerProduct<A, B> kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b)
{
    return KroneckerProduct<A, B>(a.derived(), b.derived());
}

/*!
 * \ingroup KroneckerProduct_Module
 *
 * Computes Kronecker tensor product of two matrices, at least one of
 * which is sparse
 *
 * \warning If you want to replace a matrix by its Kronecker product
 *          with some matrix, do \b NOT do this:
 * \code
 * A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
 * \endcode
 * instead, use eval() to work around this:
 * \code
 * A = kroneckerProduct(A,B).eval();
 * \endcode
 *
 * \param a  Dense/sparse matrix a
 * \param b  Dense/sparse matrix b
 * \return   Kronecker tensor product of a and b, stored in a sparse
 *           matrix
 */
template <typename A, typename B> KroneckerProductSparse<A, B> kroneckerProduct(const EigenBase<A>& a, const EigenBase<B>& b)
{
    return KroneckerProductSparse<A, B>(a.derived(), b.derived());
}

}  // end namespace Eigen

#endif  // KRONECKER_TENSOR_PRODUCT_H
